Finite Group Databasebeta

← #27193512

Subgroups — #27193512

Order 13184.

214 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15693016C211yesmaximal, characteristic
2#20267845C211yesmaximal, characteristic, complemented
3#20267841C211yesmaximal, characteristic, complemented
4#20267517C211yesmaximal, characteristic, complemented
5#20267514C211yesmaximal, characteristic
6#20267514C211yesmaximal, characteristic
7#324×C103C211yesmaximal, characteristic, complemented
8#15693016—21no—
9#15693016—21no—
10#15693016—21no—
11#15693016—21no—
12C2×C4⋊Dic103C411yescharacteristic
13C2×Dic103⋊C4C411yescharacteristic
14C2×(C2×D103)⋊C4C411yescharacteristic
15C2×(C2×D103)⋊C4C411yescharacteristic
16C2×(C2×D103)⋊C4C2211yescharacteristic
17C2×C4×Dic103C2211yescharacteristic
18Dic103⋊C8—21no—
19Dic103⋊C8—21no—
20C22⋊(C103⋊C8)C2211yescharacteristic
21C22⋊(C103⋊C8)C2211yescharacteristic
22#15692931—21no—
23C8×Dic103—21no—
24C2×C4⋊C4×C103C2211yescharacteristic
25C22⋊C8×C103C2211yescharacteristic
26C22⋊C8×C103C2211yescharacteristic
27C23×D103C2×C411yescharacteristic
28C22×Dic103C2×C411yescharacteristic
29C22×Dic103C2×C411yescharacteristic
30C22×Dic103C2×C411yescharacteristic
31C2×C103⋊C8—21no—
32C2×C103⋊C8—21no—
33C4⋊Dic103—21no—
34C4⋊Dic103—21no—
35Dic103⋊C4—21no—
36Dic103⋊C4—21no—
37(C2×D103)⋊C4—21no—
38(C2×D103)⋊C4—21no—
39(C2×D103)⋊C4—21no—
40(C2×D103)⋊C4—21no—
41(C2×D103)⋊C4—21no—
42(C2×D103)⋊C4—21no—
43C4×Dic103D411yescharacteristic
44C4×Dic103D411yescharacteristic
45C4×Dic103D411yescharacteristic
46C4×Dic103D411yescharacteristic
47C22×C4×C103C2×C411yescharacteristic
48C22×C4×C103C2×C411yescharacteristic
49C22×C4×C103C2311yescharacteristic
50C2×C8×C103—21no—
51C2×C8×C103—21no—
52C4⋊C4×C103—21no—
53C4⋊C4×C103—21no—
54C23×C103C22×C411yescharacteristic
55C22×D103—21no—
56C22×D103—21no—
57C22×D103—21no—
58C22×D103—41no—
59C22×D103—41no—
60C2×C4×C103—21no—
61C2×C4×C103—21no—
62C2×C4×C103—21no—
63C2×C4×C103—21no—
64C2×C4×C103—41no—
65C2×C4×C103—41no—
66C2×C4×C103C2×D411yescharacteristic
67C2×C4×C103C2×D411yescharacteristic
68C2×Dic103—21no—
69C2×Dic103—21no—
70C2×Dic103—21no—
71C2×Dic103—41no—
72C2×Dic103—41no—
73C2×Dic103C22⋊C411yescharacteristic
74C2×Dic103C22⋊C411yescharacteristic
75C2×Dic103C22⋊C411yescharacteristic
76C2×Dic103C22⋊C411yescharacteristic
77C8×C103—41no—
78C8×C103—41no—
79C103⋊C8—41no—
80C103⋊C8—41no—
81C22×C103—21no—
82C22×C103—21no—
83C22×C103C2×C22⋊C411yescharacteristic
84C22×C103#13111yescharacteristic
85C22×C103#13111yescharacteristic
86C2×D103—41no—
87C2×D103—41no—
88C2×D103—41no—
89C2×D103—81no—
90C2×D103—81no—
91C4×C103—21no—
92C4×C103—21no—
93C4×C103—41no—
94C4×C103—41no—
95Dic103—21no—
96Dic103—21no—
97Dic103—21no—
98Dic103—21no—
99Dic103—41no—
100C2×C103—21no—
101C2×C103—21no—
102C2×C103#40811yescharacteristic
103C2×C103#41011yescharacteristic
104C2×C103#41311yescharacteristic
105D103—81no—
106#1473—1031nomaximal, Sylow
107C103#147311yescharacteristic, complemented, Sylow
108C2×#126—1031no—
109#432—1031no—
110#431—1031no—
111#324—1031no—
112#324D10311yescharacteristic, complemented
113#323—1031no—
114#323—1031no—
115#126—2061no—
116#126—2061no—
117#126—2061no—
118#126—2061no—
119C2×C4⋊C4—1031no—
120C2×C4⋊C4—1031no—
121C2×C4⋊C4C2×D10311yescharacteristic
122C2×C22⋊C4—1031no—
123C2×C22⋊C4—1031no—
124C2×C22⋊C4—1031no—
125C2×C42—1031no—
126C4⋊C8—2061no—
127C4⋊C8—2061no—
128C22⋊C8—1031no—
129C22⋊C8—1031no—
130C22⋊C8C2×D10311yescharacteristic
131C22⋊C8C2×D10311yescharacteristic
132#97—2061no—
133C4×C8—2061no—
134C24—1031no—
135C22×C4—1031no—
136C22×C4—1031no—
137C22×C4—1031no—
138C22×C4C4×D10311yescharacteristic
139C22×C4C4×D10311yescharacteristic
140C22×C4C22×D10311yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—2061no—
144C2×C8—2061no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—2061no—
148C4⋊C4—2061no—
149C4⋊C4—2061no—
150C4⋊C4—2061no—
151C22⋊C4—2061no—
152C22⋊C4—2061no—
153C22⋊C4—2061no—
154C22⋊C4—2061no—
155C22⋊C4—2061no—
156C22⋊C4—2061no—
157C42—1031no—
158C42—1031no—
159C42—1031no—
160C42—1031no—
161C23—4121no—
162C23—4121no—
163C23—2061no—
164C23—2061no—
165C23—2061no—
166C23C2×C4×D10311yescharacteristic
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—1031no—
174C2×C4—1031no—
175C2×C4—1031no—
176C2×C4—1031no—
177C2×C4—4121no—
178C2×C4—4121no—
179C2×C4—2061no—
180C2×C4—2061no—
181C2×C4—2061no—
182C2×C4D4×D10311yescharacteristic
183C2×C4D4×D10311yescharacteristic
184C8—41no—
185C8—41no—
186C8—4121no—
187C8—4121no—
188C22—21no—
189C22—21no—
190C22—8241no—
191C22—8241no—
192C22—4121no—
193C22—4121no—
194C22—4121no—
195C22C22⋊C4×D10311yescharacteristic
196C22#1569302711yescharacteristic
197C22#1569302911yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—4121no—
203C4—2061no—
204C4—2061no—
205C4—2061no—
206C4—2061no—
207C2—21no—
208C2—21no—
209C2—8241no—
210C2#2026775611yescharacteristic
211C2#2026776311yescharacteristic
212C2#2026777411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D103
commutatorC23×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#324×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC23×D103C2×C4
cosocleC22×C4×C103C23
hypercenter#324D103
hypocenterC103#1473
LCSG ▷ C23×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #20267845C2semidirect
3. #20267841C2semidirect
4. #20267517C2semidirect
7. #324×C103C2semidirect
107. C103#1473semidirect
112. #324D103semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#156930162
#202678452
#202678412
#202675172
#202675142
#324×C1032
#1473103